Data visualization tools have been used to find properties of and relations between data elements in large datasets. For example, biologists may use data visualization tools to understand the relationships between groups of genes in the human genome, social scientists may use visualization tools to study interactions between communities of people in social networks, and machine learning experts sometimes explore how data has been categorized using data visualization tools.
One approach used in data visualization tools is to visually represent sets. Several techniques have been used to visually represent sets, and these techniques can influence how people perceive properties of individual elements and relationships between elements. Consider Euler or Venn diagrams, which are commonly used set representations. While sometimes effective, visual set representations with these types of diagrams often overlap due to membership intersection, and excessive intersections or overlaps may cause these diagrams to lose their expressive qualities. That is, when numerous sets intersect with each other, most types of set representations become difficult to read.
FIG. 1 shows an example Venn diagram 100. Points 102 (also referred to as graphic nodes) represent data elements that belong to sets represented by regions 104. In the example of FIG. 1, points 102A belong only to a set represented by region 104A. As seen in area 106, where many regions 104 overlap, it can be difficult to interpret the relevant data and the relations between sets. Enhancements such as color, transparency, and texture may not fully address the problem of visual comprehension when many intersecting sets are displayed. Previous methods for visually representing sets may have other shortcomings, and there is a general need for set representations that are readily grasped and which facilitate new ways of understanding interrelated sets of data. Consequently, techniques related to linear representations of sets are discussed below.